1. Characteristics of Functions

2. Standard
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

3. Objectives SWBAT determine the domain and range of a function
SWBAT determine the x and y intercepts of a linear function
SWBAT determine whether a linear function is increasing or decreasing

4. Characteristics of Functions
Domain and Range!
Intercepts!
Increasing and Decreasing!

5. Domain and Range Domain
-The set of x-coordinates of the set of points on a graph.
Range
-The set of all possible outputs (y-values) of a function or graph.
Discrete (points) graphs
– you just LIST the domain and range
Continuous (lines or curves) graphs
– you use interval notation

6. Are used when there is a open dot or the number is NOT included on the graph.
Are used when there is a closed dot or when the number is included on the graph.

7. Domain and Range: Graph
[-8, -4, 2, 8]
[-4, -2, 8]

8. Domain and Range: Graph
[-3, 2)
[-5, 2]
*Notice the open and closed circles at the end points. Any point in the graph is considered closed.

9. Domain and Range: Graph
[-4, ∞)
[-3, ∞)
If there is no circle, assume it is an arrow, which is used with open parenthesis.

10. Domain and Range: Graph
Any point in the graph is considered closed.

11. Intercepts (aka “zeros”)
x-intercept – the point at which the line intersects the x-axis at (x, 0)
y-intercept – the point at which the line intersects the y-axis at (0, y)
Zeros are the same thing as the x- intercepts.

12. Example 1: Find the y-intercept

13. Example 2: Finding the Zeros

14. Increasing/Decreasing Behavior
Move left to right
If your finger is moving UP then the function is increasing
If your finger is moving DOWN then the function is decreasing
If your finger is moving only sideway, then your function is constant.

15. Examples: Are the functions increasing, decreasing or neither?